New York Times

WASHINGTON — There are lots of open questions about the road the Supreme Court justices will take to a final decision about whether the Constitution guarantees a right to same-sex marriage. But one thing seems clear: The answer will arrive next June.

The endgame started Monday morning. At their first private conference of the term, the justices were scheduled to consider, among many other things, seven petitions urging them to hear appeals from decisions striking down bans on same-sex marriage.

In an unusual move, the same-sex couples on the winning side of those cases joined their adversaries in asking the Supreme Court to settle the question, nationally and once and for all.

The justices face complicated choices about which case to accept, and when. They could announce their choices as soon as this week and hear arguments as soon as January.

Or they could sort and sift and wait for other courts to rule. The last time the court heard cases on same-sex marriage, in 2013, they wereargued in March. The last argument session of the term is in April.

The justices could hear a single case or all of them. They could schedule one hour of arguments or several. They could ask for separate arguments on various legal theories.

So many variables, but one bottom line: “I think the court is going to give a definitive answer this term,” said Irving L. Gornstein, the executive director of Georgetown’s Supreme Court Institute.

The justices are not starting from scratch. They immersed themselves in the legal issues surrounding same-sex marriage last year, though they ended up ducking the question of what the Constitution had to say about it. Why, then, will it most likely take the whole term to render a decision this time?

The justices often say that decisions are issued as soon as the opinions are ready, and former Supreme Court law clerks confirm this.

“I can’t think of an instance, certainly during my term, that the court sat on an opinion when it was done,” said Geoffrey R. Stone, a law professor at the University of Chicago who served as a clerk to Justice William J. Brennan Jr. “It’s inconceivable.”

Yet the biggest cases seem to land at the end of June, just before the court’s summer break.

In 2013, for instance, the three final days of the term felt like the judicial equivalent of sweeps week on network television.

Monday: affirmative action. Tuesday: voting rights. Wednesday: gay rights.

The answer may be as simple as human nature. “The court uses as much time as they have to decide the really important cases,” saidDeanne E. Maynard, a lawyer with Morrison & Foerster who served as a law clerk to Justices Lewis F. Powell Jr. and Stephen G. Breyer.

The end-of-term crunch for big cases is the subject of a new study to be published in The Duke Law Journal. Though the study considered 7,219 cases from 1946 to 2013, it turned out to be surprisingly hard to show with data what everyone knows from experience.

The question is not, after all, whether any particular case is more likely to be decided late in the term — more than 30 percent of the court’s decisions are issued in June and more than half of those in the last week of the month.

The question, rather, is whether big cases are disproportionately likely to come late. That requires, for starters, an objective definition of significance. The study used several measures, including coverage on the front page of this newspaper, the number of friend-of-the-court briefs filed and how often the decision was cited in later Supreme Court opinions.

All of those measures confirmed that big decisions were disproportionately likely to come in late June.

But perhaps big cases are also more complicated and divisive, meaning that it would take longer to decide them whether they were significant or not. They are, the study concluded, but this explained only part of the phenomenon.

The study’s authors — Lee Epstein of Washington University in St. Louis, William M. Landes of the University of Chicago and Judge Richard A. Posner of the federal appeals court in Chicago — offered three possible reasons for waiting so long to decide the biggest cases.

One is that justices keep polishing the opinions that will define their legacies until the last possible moment. (Indeed, as Prof. Richard J. Lazarus of Harvard Law School demonstrated recently, some keep polishing years later.)

A second possibility is that releasing several major decisions in quick succession, some liberal and some conservative, “may tend to diffuse media coverage and other commentary of any particular case, and thus spare the justices unwanted criticism.”

Or perhaps the explanation is more personal: “The justices, most of whom have busy social schedules in Washington, may want to avoid tensions at their social functions by clustering the most controversial cases in the last week or two of the term — that is, just before they leave Washington for their summer recess.”

The court has released its calendar for the new term, and it may contain all the data you need to predict when the court will determine whether there is a constitutional right to same-sex marriage. The last day on the schedule is June 29, 2015.